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bloodstream by 1 mg/liter. mt+1 = 1mt + 1 with m0 = 0. 3 The Excel parts of this project need to be done in Excel, Open Office or any other spreadsheet software and printed and attached to the rest of your work. The rest of the project may be typed or hand-written, in a neat and legible way (messy work can cost you up to 5 points.) The first page of the project needs to contain the name(s) and student number(s) of the authors of the project clearly written on the top. Include the question numbers with your answers. Projects consisting of more than one page need to be stapled! Everything is due in hard copy in class or in your professor's office in the Chase Building by 5 PM on October 3, 2012. Medication in the Bloodstream In class we studied the following model for the level of medication in the bloodstream of a patient who receives a fixed daily dose of medication, that raises the concentration of the medication in the The equation m0 = 0 means that on day 0 (before the treatment starts) there is no medication in the blood. The '+1' represents the dosage and the 1 is the fraction of medication left in the 3 bloodstream by the patient's body tissue each day (which means the other 2 is absorbed out). 3 The fraction of the medication that is absorbed out of the blood into the tissue can be different for different people. Below we explore what would happen if the patient absorbed more of the medication. 1. Assume that the patient absorbs 80% of the medication that is present in the bloodstream (so 80% of what is in the blood stream on day t is absorbed out of the bloodstream into the tissue by the next day, t + 1). The daily dose is still 1 mg/liter, and the patient begins with no medication in the blood on day 0. Give the new discrete dynamical system that models this situation (including the initial condition). Note: For the remaining questions in this section assume the discrete dynamical system is given by mt+1 = .25mt + 1 with m0 = 0 . 2. Write an excel document that calculates the medication levels in the bloodstream for the first two weeks of taking this medication (i.e., for 14 days). What do you expect to happen with the amount of medication in the bloodstream if the patient continues to take this dose of medication for a longer period of time? 3. How is this different from what happened for the first system (mt+1 = 1 mt + 1)? What 3 conclusions can you draw about the relationship between the level of absorption by the body tissues and the final levels of the medication concentration? Does this make sense? 4. Find the equilibrium point(s) of this system. How is this related to the answer of your previous question? 5. Draw a cobwebbing diagram that determines whether this equilibrium is stable or unstable. Does this answer agree with what you would have expected from your Excel table? For questions 6-8, we change the daily dose. For a daily dose of d mg/liter the system is given by: mt+1 = .25mt + d , with m0 = 0 . 6. What would the equilibrium concentration be in this case? Give your answer as a function of d. 7. Suppose that a doctor wants to give the patient a daily dose such that eventually the concen- tration of medication will be 2 mg/liter. What should that dose be?
he log was 210 feet ahead of you when you noticed it, which unfortunately wasn't soon enough.
angle of elevation to the top of the tree to be 53°. What is the height of the tree? Round your answer to the nearest foot.
Prove that if f is a differentiable function with f´(x) > 1 for all x, then there is at most one c such that f(c) = c. [Use the Mean Value Theorem]
a month for its economy plan The equation c=20t + 30 describes the total cost c of operating a media services phone for t month
A company wishes to manufacture a box with a volume of 36 square feet that is open on the top and is twice as long as it is wide. Find the dimensions of the box produced from the minimal amount of the material.
What systems of equations can be solved by graphing or using substitution or elimination? Which method do you like best and why would it be different method. How would you answer this question?
A circle is the set of points that lie at a constant distance from one point, the center of the circle. This solution explains the equation of a circle with a center point that can exist anywhere on the coordinate plane.
A plane is heading due south with an airspeed of 229 mph. A wind from a direction of 52 degrees is blowing at 13 mph. Find the direction the plane is actually headed. (Note that bearings are measured from north, clockwise.
How many 3-letter codes can be formed using the letters A,B,C,D and E?
A pilot flies south 100 miles then east 100 miles then north 100 miles and ends up back where she started. Where might she have started?
An expensive fencing along the lots length costs $20 per fott and an inexpensive fencing along the two side widths costs only $8 per foot. the total cost of the fencing along the three sides comes to $3280. What is the area of the lot?
Select the ordered pair from the choices below that is a solution to the following system of equations.
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